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XIV. On the Definition of the Terms ^^ Energy'''' and " IFor/;." 

 Btj Simon Newcomb*. 



THE accepted definitions of the terms " kinetic energy '^ 

 and " work " are substantially these : — 



The kinetic energy of a moving body is measured by half 

 the product of its mass into the square of its velocity. 



The work done by a force acting upon a body is the pro- 

 duct of the intensity of the force into the motion of the body 

 in the direction in which the force acts. 



It will be noticed that the terms " velocity " and " motion " 

 are here used as if their measures were absolute. But it is 

 universally understood that motion, and therefore velocity, 

 are relative terms ; that no body considered in itself can be 

 said to be either in motion or at rest, because motion and rest 

 can be defined only as the motion or rest of one body rela- 

 tively to some other body, real or imaginary. It follows that 

 we may assign to any one body any arbitrary motion we 

 choose. 



Such being the case, it would seem to follow from the above 

 definitions that the energy of a moving body considered by 

 itself is an entirely arbitrary quantity ; that the same is true 

 of the work done upon a body ; and that, when we consider 

 the kinetic energy of a system, its amount will depend upon 

 the origin to which we refer the motion of the system. The 

 value of the kinetic energy will be a minimum when the 

 motion which we assign to the centre of gravity of the system 

 is zero, and may be greater than this minimum by an amount 

 which will depend upon the motion of the centre of gravity 

 relative to the point of reference. Not only is the work done 

 by a force acting on a moving body arbitrary for the same 

 reason, but we cannot assign any value to the work necessary 

 to change one given motion A into another given motion B, 

 though the relation of B to A be completely given. 



The question now arises, In what form are we to define 

 these seemingly arbitrary quantities so as to make their 

 amounts definite? This requires an improved statement of 

 Newton^s third law. As usually formulated, this law implies, 

 but does not completely express, a universal condition of the 

 action of every mechanical force with which we are acquainted, 

 namely : — 



Ko force ever acts except Letween bodies ; and every force so 

 acting on a hody A is a mutual action between that body and 

 some other body B, such that the actions on the two bodies are 

 equal and opposite. 



* Communicated by tlie Author. 

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